I had been planning to work for 20 hours a week for 12 weeks this summer to earn $\$3000$ to buy a used car. Unfortunately, I got sick for the first two weeks of the summer and didn't work any hours. How many hours a week will I have to work for the rest of the summer if I still want to buy the car?
Solution: If the total amount that I earn for the summer is constant, then the number of hours I work each week and the total number of weeks that I work are inversely proportional. Consequently, if I only work $\frac{10}{12}=\frac56$ as many weeks, I need to work $\frac{6}{5}$ as many hours each week. $\frac{6}{5}\cdot20=24$, so I need to work $\boxed{24}$ hours a week.